Also adds a section in the docs explaining the `sentinel` logcontext.
Spawning from https://github.com/element-hq/synapse/pull/18870
### Testing strategy
1. Run Synapse normally and with `daemonize: true`: `poetry run
synapse_homeserver --config-path homeserver.yaml`
1. Execute some requests
1. Shutdown the server
1. Look for any bad log entries in your homeserver logs:
- `Expected logging context sentinel but found main`
- `Expected logging context main was lost`
- `Expected previous context`
- `utime went backwards!`/`stime went backwards!`
- `Called stop on logcontext POST-0 without recording a start rusage`
- `Background process re-entered without a proc`
Twisted trial tests:
1. Run full Twisted trial test suite.
1. Check the logs for `Test starting with non-sentinel logging context ...`
* Pull Sentinel out of LoggingContext
... and drop a few unnecessary references to it
* Factor out LoggingContext.current_context
move `current_context` and `set_context` out to top-level functions.
Mostly this means that I can more easily trace what's actually referring to
LoggingContext, but I think it's generally neater.
* move copy-to-parent into `stop`
this really just makes `start` and `stop` more symetric. It also means that it
behaves correctly if you manually `set_log_context` rather than using the
context manager.
* Replace `LoggingContext.alive` with `finished`
Turn `alive` into `finished` and make it a bit better defined.
